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Fursaev, Dmitri; Vassilevich, Dmitri

Operators, Geometry and Quanta Methods of Spectral Geometry in Quantum Field Theory (Gebundene Ausgabe)

Reihe: Texts and Monographs in Physics

Springer-Verlag GmbH, Springer Netherland, Juni 2011

286 S. - Sprache: Englisch - 5 schwarz-weiße Abbildungen - 242x167x23 mm

ISBN: 9400702043 EAN: 9789400702042

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

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Bridges the physical applications of heat kernel theories with the mathematical foundationsSome material, e.g. non-linear spectral problems, appears for the first time in a monograph formExamples from the forefront of current research (quantum solitons, noncommutativity, etc) worked out in detail


1 Preface.- 2 Notation Index I The Basics: 3 Geometrical Background.- 4 Quantum fields II Spectral geometry: 5 Operators and their spectra.- 6 Spectral functions.- 7 Non-linear spectral problems.- 8 Anomalies and Index Theorem III Applications: 9 Effective action.- 10 Anomalies in quantum field theories.- 11 Vacuum energy.- 12 Open strings and Born-Infeld action.- 13 Noncommutative geometry and field theory IV Problem solving: 14 Solutions to exercises.

Über den Autor

The authors D. Vassilevich and D. Fursaev are acknowledged experts in spectral geometry and quantum gravity. D. Fursaev has published more than 60 articles in high profile science journals, and he was appointed the rector of Dubna International University in 2008. D. Vassilevich is a professor for mathematical physics at the Universidade Federal do ABC, Santo Andre (Brazil). He published more than 100 articles in scientific journals and is author of the book ""Fundamental Interactions - A Memorial Volume for Wolfgang Kummer" (2009).


From the reviews:"The authors have tried to make the book as self-contained as possible with the declared purpose that it should be useful for both active researchers and graduate students. The inclusion in the book of more than a hundred exercises with their solutions makes it indeed possible to use the material in it for lecture courses on physical applications of the spectral theory. ... This is a good book, unique in several ways, clearly written ... and also a very useful reference for practical purposes." (Emili Elizalde, Mathematical Reviews, Issue 2012 f)"This book represents an introduction into the theory of spectral functions and their applications to quantum field theory (QFT). ... more than a hundred exercises with their solutions help the reader to understand better the topic and makes possible the use of this book in lecture courses on physical applications of the spectral theory. ... Noncommutative theories are a beautiful example of how physics and mathematics have a mutual influence. Each chapter contains exercises, which are integer part of the book." (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1230, 2012)

ISBN 9-400702-04-3, ISBN 9-40-070204-3, ISBN 9-40070-204-3, ISBN 9-400-70204-3, ISBN 9-4007-0204-3

ISBN 978-9-400702-04-2, ISBN 978-9-40-070204-2, ISBN 978-9-40070-204-2, ISBN 978-9-400-70204-2, ISBN 978-9-4007-0204-2

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